KR20200093975A - System and Method for Data Processing using Sphere Generative Adversarial Network Based on Geometric Moment Matching - Google Patents

Abstract

The present invention relates to an apparatus and a method for data processing using a generative adversarial network on a sphere through geometric moment matching, which can solve a problem on a gradient restriction by assuming that a feature space of a determination network is a sphere and minimizing a multi-dimensional moment on the same. The apparatus comprises: a generator receiving a value from a random noise z to generate fake data and transfer the fake data to a discriminator; the discriminator receiving real data and the fake data to be trained; and a geometric moment matching unit receiving final data from the discriminator, mapping the final data with an n-dimensional Euclidean feature space, mapping each feature point of the fake data and the real data into an n-dimensional hypersphere again by geometric conversion, and allowing a sphere GAN to calculate the geometric moment centering on the north pole of the hypersphere by using mapped points, wherein the discriminator attempts to maximize a moment difference of probability measurement between the real and the fake data, and the generator attempts to minimize the moment difference to interfere with the discriminator such that training is performed.

Description

System and Method for Data Processing using Sphere Generative Adversarial Network Based on Geometric Moment Matching}

The present invention relates to a generation model that is a sub-field of machine learning and computer vision. Specifically, it is assumed that the feature space of the discriminant network is a sphere, and the geometric moment matching is performed to minimize the multi-order moment thereon to solve the problem of the gradient constraint. It relates to a data processing apparatus and method using a hostile generation network on the sphere through.

Generative Adversarial Networks (GANs) provide a wide range of computer vision to provide a variety of features such as image creation, super resolution, video prediction, style delivery, visual tracking, 3D reconstruction, segmentation, object detection, augmented learning and medical imaging. It is used to achieve high performance in applications.

This hostile generation network has received much attention since it was first introduced in 2014 by Ian J. Goodfellow.

Unlike traditional deep learning algorithms such as CNN and RNN, GAN generates image and voice data using a comparative learning method.

The principle of operation is that different subjects, consisting of generators and discriminators, compete against each other and maximize their performance. Through this process, it is a principle to generate fake data close to real data.

Using GAN, you can restore a low-quality image or create a completed image with a simple sketch. In reality, the GAN model can be used for automating the inspection of disasters that absolutely lacks the necessary data for learning.

The prior art GAN attempts to minimize the difference in distribution between fake data and real data. To this end, a generator attempts to generate a desired sample that looks like real data, and a discriminator attempts to differentiate it from real data. do.

These GANs have been successfully applied to various tasks, but training them is very difficult. Therefore, it is difficult to solve more complex problems using GAN.

As such, hostile adversarial networks (GANs) are networks for generating models, which are sub-fields of machine learning and computer vision, and various studies have been conducted to improve the quality of generated images similar to actual images.

In order to solve the problems of the first GAN, various technologies such as DCGAN, LSGAN, and WGAN have been proposed. GAN, which has been developed in this way, is used not only in academia but also in the real IT industry as a whole, and it creates various values, especially in the field of image processing.

However, the Wesserstein distance is used to reduce the difference between the probability measure representing the actual data and the probability measure created by the generating network. To this end, the gradient of the discriminant network is restricted.

This can be helpful for training, but it limits the capacity of the network, and it does not take full advantage of the neural network's characteristics, which leads to poor performance.

Therefore, there is a need to develop a data processing technology that uses a hostile generation network of new technologies to solve the problem of gradient constraints.

Republic of Korea Registered Patent No. 10-1843066 Republic of Korea Patent Publication No. 10-2018-0120478

The present invention is to solve the problem of the data processing technology using the hostile generation network of the prior art, assuming that the feature space of the discriminant network is a sphere, and minimizes the multi-order moment thereon to solve the problem of the gradient constraint. An object of the present invention is to provide a data processing apparatus and method using a hostile generation network on a sphere through moment matching.

The present invention is an old GAN (sphere GAN) of a new concept that provides several advantages over a general IPM-based GAN, so that the behavior of a trained network can be predicted by newly defining a metric between well-defined metrics. An object of the present invention is to provide a data processing apparatus and method using a hostile generation network on a sphere through geometrical moment matching.

The present invention uses Riemannian manifolds to define the integral probability metrics (IPM) in the GAN objective function. It is an object of the present invention to provide a data processing apparatus and method using the hostile generation network above.

The present invention enables a stable training by binding the IPM in the objective function using algebraic functions in Sphere GAN, and provides a more accurate result by utilizing high-dimensional statistical data using geometric moment matching. The objective is to provide a data processing apparatus and method using a hostile generation network on a sphere through matching.

Sphere GAN according to the present invention can efficiently match high-order moments in a feature space, greatly improving accuracy, and generating images almost similar to real-life images through a generation network in image sets for real objects such as CIFAR-10 and STL-10. An object of the present invention is to provide a data processing apparatus and method using a hostile generation network on a sphere through geometric moment matching.

Other objects of the present invention are not limited to those mentioned above, and other objects not mentioned will be clearly understood by those skilled in the art from the following description.

A data processing apparatus using a hostile generation network on a sphere through geometric moment matching according to the present invention for achieving the above object generates a fake data by accepting a value from a random noise z and determines the generated fake data as a discriminator Generator to deliver; Discriminator to train by receiving real data (x) and fake data; Mapping to n-dimensional Euclidean feature space by receiving final data from the discriminator, and geometric transformation of feature points of fake and real data respectively Containing a geometric moment matching unit for re-mapping by n-dimensional hypersphere by, and using the mapped points to calculate the geometric moment centered on the north pole of the hypersphere with the spherical GAN. The discriminator is characterized in that it attempts to maximize the moment difference in probability measurement between real and fake data, and the generator attempts to interfere with the discriminator by minimizing the difference in moment.

A data processing method using a hostile generation network on a sphere through geometric moment matching according to the present invention for achieving a different purpose assumes that a feature space of a discrimination network is a sphere, and minimizes multi-dimensional moments thereon to achieve Generating fake data that is similar to real by receiving a value from random noise z in the generator using a spherical GAN that newly defines a metric to predict the behavior of a trained network; discriminates the fake data generated in the generator Passing the data to the machine; training the discriminator to receive real data and fake data and mapping them to the n-dimensional Euclidean feature space; each of the feature points of the fake data and the real data is converted back to the n-dimensional hypersphere by geometric transformation. Mapping; using a mapped point, the spherical GAN calculates the geometric moment centered on the north pole of the hypersphere; the discriminator of the spherical GAN determines the moment difference in the probability measurement between real and fake samples And attempting to maximize, and the generator attempting to interfere with the discriminator by minimizing moment differences.

The data processing apparatus and method using a hostile generation network on a sphere through geometric moment matching according to the present invention as described above has the following effects.

First, assuming that the feature space of the discriminant network is a sphere, the multi-order moment is minimized to solve the problem of the gradient constraint.

Second, by using a new concept of sphere GAN (sphere GAN), which provides several advantages over general IPM-based GAN, mathematically defined metrics between well-defined measures are newly defined to predict the behavior of trained networks. do.

Third, in order to define integral probability metrics (IPM) in the GAN objective function, Riemannian manifolds are used to enable stable training without using gradient penalty or virtual data sampling techniques.

Fourth, Sphere GAN uses algebraic functions to bind the IPM in the objective function so that it can be trained stably, and geometrical moment matching is used to provide more accurate results using high-dimensional statistical data.

Fifth, Sphere GAN efficiently matches high-order moments in the feature space to greatly improve accuracy, so that images generated for real-world objects such as CIFAR-10 and STL-10 can be generated to generate images almost similar to real-life images through a generation network. do.

1 is an overall configuration diagram of a data processing apparatus using a hostile generation network on a sphere through geometric moment matching according to the present invention
2 is a configuration diagram for explaining a stereographic projection (stereographic projection) that is an example of a geometric transformation function according to the present invention
Figure 3 is a flow chart showing a data processing method using a hostile generation network on a sphere through geometric moment matching according to the present invention
4 is a graph of the evaluation results according to the dimension and matching mode of the hypersphere using IS (Inception scores)
5 is a gradient characteristic graph of Sphere GAN and WGAN-GP discriminator network
6 is a graph comparing the average calculation time repeated 100 times for different GAN variants
7A and 7B are qualitative results of the old GAN of the LSUN-bedroom data set and the qualitative results of the old GAN of the STL-10 data set.

Hereinafter, a preferred embodiment of a data processing apparatus and method using a hostile generation network on a sphere through geometric moment matching according to the present invention will be described in detail as follows.

Features and advantages of a data processing apparatus and method using a hostile generation network on a sphere through geometric moment matching according to the present invention will become apparent through detailed description of each embodiment below.

1 is an overall configuration diagram of a data processing apparatus using a hostile generation network on a sphere through geometric moment matching according to the present invention.

In the present invention, assuming that the feature space of the discriminant network is a sphere, a multidimensional moment is minimized thereon to newly define a metric between well-defined measures to predict the behavior of a trained network. CIFAR-10, STL- The goal is to create an image that is almost the same as the real world through the creation network from the image set of the 10th real object.

The present invention relates to a hostile adversarial network, which is one of the generation models, which are sub-fields of machine learning and computer vision, and discriminates GANs that distinguish between real data and fake data. The discriminator includes a configuration that maps the final data to a sphere, and a configuration that calculates the distance by mapping the final data to a sphere, and uses the existence of a bound of distance. This is to enable stable GAN learning.

A data processing apparatus using a hostile generation network on a sphere through geometric moment matching according to the present invention is a fake generated by generating a real-like image (fake data) by receiving a value from a random noise z, as shown in FIG. A generator 100 that delivers data to the discriminator 200, a discriminator 200 that receives and trains real data and fake data, maps it to an n-dimensional Euclidean feature space, and fake and real samples, respectively. The geometric moment matching unit calculates the geometric moment centered on the north pole of the hypersphere by using the mapped points to map the feature points back to the n-dimensional hypersphere, and using the mapped points. (300), the discriminator 200 of the old GAN attempts to maximize the moment difference in probability measurement between real and fake samples, and the generator 100 attempts to interfere with the discriminator by minimizing the moment difference to train will be.

First, when z enters the generator 100, a fake image is generated and transmitted to the input of the discriminator 200.

Thereafter, through the LReLu (31), Avg Pooling (32), and Dense (33), through the ISP (Inver stereographic projection), it maps to the sphere 34 as shown above.

At this time, the ISP is responsible for mapping the points of the plane that is the output of the Dense to the points on the sphere.

Fig. 1 shows the pipeline structure of the old GAN, and the fake data is generated from the noise input by the generator.

The actual and fake data is then sent to a discriminator to map the output to an n-dimensional Euclidean feature space (ie, a yellow plane).

The green and purple circles on the plane represent the characteristic points of the fake and real samples, respectively. By geometric transformation, these feature points are mapped back to n-dimensional hyperspheres (ie, yellow spheres).

Using these mapped points, the spherical GAN calculates the geometric moment around the north pole of the hypersphere.

The discriminator of the old GAN attempts to maximize the moment difference in the probability measurement between real and fake samples, but the generator tries to interfere with the discriminator by minimizing the moment difference.

Using geometric moments defined in the hypersphere, constructors and discriminators improve performance through a two-player mini-max game.

The hostile generation network on the sphere through geometric moment matching according to the present invention will be described in detail as follows.

The objective function based on the Westerstein metric is defined as the first moment in the one-dimensional feature space.

Here, G and D represent generators and discriminators, respectively, and P and N represent actual data and potential code distribution, respectively. In Equation 1, discriminator (D) maps data (x) to real (R), this is

Here, D must satisfy the 1-Lipschitz condition D ∈ Lip1, and X ⊂ Rn is an n-dimensional Euclidean image space.

As in the existing IPM-based GAN, the objective function of the old GAN is based on Equation (1).

Unlike the existing GAN, which directly matches the first moment in the one-dimensional feature space, the spherical GAN matches the high and multiple moments defined in the hypersphere that extends to a dimension larger than the three-dimensional.

To this end, the output of the discriminator according to the present invention is defined as follows.

Equation 1 shows the objective function form of the existing WGAN (Sphere GAN baseline).

Here, x is actual image data and z is random noise.

The generator G takes a value from the random noise z to generate an image similar to the real one, and the discriminator D receives the actual data x to train.

In such a way that the difference value expressed as above is minimized (min), the generator operates to try to minimize the'discrimination' trained by the actual discriminator, and the discriminator is trained to try to maximize (max) to discriminate it.

The objective function of the spherical GAN is as follows.

는 각 샘플과 hypersphere N의 north pole사이의 r 번째 모멘트 거리를 측정하는 것을 나타내고, 아래 첨자 s는

가

상에서 정의되어 있음을 나타낸다.Function if r = 1, ..., R

Indicates the measurement of the r-th moment distance between each sample and the north pole of hypersphere N, and the subscript s is

end

It is defined in the phase.

Using the new objective function in Equation 4, the old GAN can define the IPM on the hypersphere, thereby easing some of the constraints imposed on the discriminator.

However, the condition to be satisfied in the objective function described above is that D must be a 1-Lipschitz function.

In order to satisfy this condition, three technologies based on WGAN-GP, CT, and WGAN use the following gradient penalties.

Here, G* represents a fixed generator and C represents additional constraints defined in Table 1.

In Equation 5, all gradient norms have to be calculated every iteration, which increases the computational complexity.

Since the gradient penalty limits the capacity of the discriminator, it is necessary to accept a decrease in performance in order to satisfy the Lipschitz condition, and the present invention is to solve such a problem.

Unlike traditional approaches, older GANs do not require additional constraints to ensure that the discriminator is located in the desired function space. Using geometric transformation, the spherical GAN ensures that the distance function is in the desired function space.

The new objective function of the discriminator is:

The algorithm in Table 2 shows the pseudo-code of the old GAN according to the present invention.

The hypersphere expanded to a dimension larger than three dimensions is as follows.

에서 정의된 특징 공간을 통해 여러 모멘트를 매칭한다.As in Equation 4, the spherical GAN is a hypersphere

Match several moments through the feature space defined in.

Older GANs use hyperspheres instead of any Lehman manifold M, providing the following advantages:

는 바운드를 형성하고 구현하기가 매우 용이하다.First, the distance function of the hypersphere

It is very easy to form and implement a bound.

Second, the gradient norm works well as a distance function, which is important for stable learning.

Third, the Riemannian structure of the hypersphere is suitable for defining GAN objects.

을 전형적으로 고려한다. 이러한 GAN은 임의의 리만 매니폴드를 모델링하여 확장할 수 있다. 그러나 이러한 매니폴드는 컴팩트하지 않고 거리 함수가 바운드되지 않고, 그레디언트 폭발(gradient explosion)과 불안정한 학습을 유발할 수 있다.In contrast, a typical GAN is a Euclidean space with a Euclidean distance.

Is typically considered. This GAN can be extended by modeling any Lehmann manifold. However, these manifolds are not compact and the distance function is not bound, which can lead to gradient explosion and unstable learning.

을 초구(hypersphere)

으로 변환하는 기하학 인식 변환 함수를 사용한다.To solve this problem, the old GAN is a Euclidean space.

The hypersphere

Use a geometry-aware transform function to convert to.

This function is implemented by the last convolutional layer of the discriminator.

에서

에 이르는 미분동형사상(diffeomorphism)에 의해 설계된다. 따라서, 변환 함수는 미분 가능하고 특징 공간의 모든 점에서 차원을 보존할 수 있다.The conversion function according to the present invention is

in

It is designed by diffeomorphism leading to. Thus, the transform function is differential and can preserve dimensions at all points in the feature space.

The following describes stereographic projection as a geometric transformation function.

2 is a configuration diagram for explaining a stereographic projection (stereographic projection) that is an example of a geometric transformation function according to the present invention.

을 초구(hypersphere)

으로의 미분동형사상(diffeomorphism)이다.The inverse function of stereographic projection is the Euclidean space

The hypersphere

It is a diffeomorphism.

Intuitively, the inverse function of stereographic projection can be regarded as a method of projecting on a hyperplane.

의 좌표계를 p = (p1, ..., pn)이라고 하고, 초구(hypersphere)의 중심점(north pole)을 N = (0, ..., 1)이라고 하면,

If the coordinate system of is p = (p1, ..., pn), and the north pole of the hypersphere is N = (0, ..., 1),

은 다음과 같이 정의된다.Inverse function of stereographic projection

Is defined as

을 투영한 후, 두 점 사이의 거리를 초구(hypersphere) 메트릭 측면에서 측정한다.Two points through the inverse function of stereographic projection

After projecting, the distance between two points is measured in terms of the hypersphere metric.

는

에 정의되는 거리함수이다. 기하학적으로

는 측지 거리로 고려될 수 있다.here,

The

Is the distance function defined in Geometrically

Can be considered as the geodetic distance.

As shown in Fig. 2, the geodesic distance between two points on the hypersphere is much shorter than the Euclidean distance and bound to the hyperplane (i.e., yellow sphere), so that the sphere with the objective function in equation (4) Stable learning is possible when using GAN.

(Bo Jeong-ri 1) The distance function in Equation 8 is differentiable and bound.

The distance function in Equation (8) satisfies a non-negative value, a symmetric value, and a triangle inequality, so it can be differentiated.

The hypersphere is a compact manifold, so the distance between the two points is bound.

)For example, the Euclidean distance between two points 0 = (0, ..., 0) and q = (t, ..., t) diverges.(

)

In contrast, the distance defined in the hypersphere in Equation 8 converges.

)(

)

The geometry-recognition transformation function of the spherical GAN limits the divergence of the discriminator output to strengthen the stable training power, preserve the dimension of the feature space and maintain the discrimination.

The mathematical analysis of the old GAN is as follows.

First, the connection to the IPM is as follows.

It proves that minimizing the objective function of Equation 4 is minimizing IPM.

To do this, we define the geometric center moment for the Riemannian manifold.

M is a small, connected, geodetically complete Riemann manifold with Borel σ algebra, Σ.

와

는 모두 측정 가능한 공간 (M, Σ)에 정의된 확률 측정치이다.

Wow

Is a probability measurement defined in the measurable space (M, Σ).

IPM is defined as follows.

와

사이의 거리 측정값이다.(Definition 1) IPM is a measure of two probability

Wow

It is a measure of the distance between.

Here, F is a class of an actual value boundary measurable function for M.

The geometric moment for M is defined as follows.

의 r 번째 중심 모멘트는 다음과 같다.(Definition 2) Top of (M, Σ) for given point p ₀

The r th center moment of is

및

이다.here,

And

to be.

은 M에서의 리만 거리 함수(Riemannian distance function)이다.

Is the Riemannian distance function in M.

와

사이의 새로운 IPM을 다음과 같이 정의한다.In the old GAN

Wow

The new IPM is defined as follows.

(Definition 3)

The IPM based on the moment difference is as follows.

은 주어진 점 p₀에서 다른 점으로부터의 유한 거리 함수(bounded distance functions)의 클래스이다.here,

Is a class of bounded distance functions from another point at a given point p ₀ .

When comparing (Definition 1) and (Definition 3), consider the relationship between the previous IPM and the IPM of the old GAN.

는 수학식 4의

에 해당하지만, M은

으로 대체될 수 있고,

는 중심점(north pole) N으로 설정할 수 있다.Equation (11)

Equation 4

Corresponds to, but M is

Can be replaced by,

Can be set to the north pole (N).

Then, we obtain the equation as in Equation 4. This means that minimizing the objective function of Equation 4 is minimizing IPM in Equation 11.

However, there are some differences between the old IPM and the old GAN's IPM.

을 중심으로 한 M상의 한정된 거리 함수의 집합이다.IPM function space according to the present invention

It is a set of limited distance functions of M phase centered on.

Therefore, the old GAN parameterizes the distance function as follows.

Here, {xi} is a set of images. In contrast, the functional space of WGAN's IPM is a set of 1-Lipschitz discriminators.

Therefore, parameterizing the discriminator is as follows.

이다.here,

to be.

And the link to the Westerstein street is as follows.

은 수학식 11에서 정의된 구형 GAN의 IPM이며, 여기서

이다.

Is the IPM of the old GAN defined in Equation 11, where

to be.

를 감소시키는 것을 목적로 하는데, 이는

에 정의된 두 가지 확률 측정

와

사이의 고차 중심 모멘트를 매칭시키는 것과 상응한다.The generator of the old GAN

It aims to reduce the

Two probability measures defined in

Wow

Corresponds to matching the higher order center moment between.

가 약하게

에 수렴한다.(Proposition 1)

Weakly

Converge on.

를

에 정의된 확률 측정의 r-웨서스테인 거리라 한다.

To

It is called the r-western distance of the probability measurement defined in.

을 최소화하는 것은 모든 r에 대해 r-웨서스테인 거리의 합계를 최소화하는 것과 같다.after that

Minimizing is equal to minimizing the sum of r-western distances for all r.

이 0으로 수렴한다.(Proposition 2)

This converges to zero.

In the conventional GAN based on Westerstein distance, the objective function is designed in a dual form by the Kantorovich-Rubinstein duality theorem. In the dual form, for efficient learning of the GAN, it can be implemented only with 1-Wesserstein distance.

Unlike the conventional GAN, the spherical GAN region can use a more general r-Wesserstein distance, so the function space is much wider.

And the gradient analysis is as follows.

을 사용하면, 구형 GAN은

의 다른 모멘트를 선택하여 손실 함수(loss functions)의 그레디언트를 계산할 수 있다.Than other IPM

Using, the old GAN

You can calculate the gradient of the loss functions by selecting another moment of.

When different moments are selected, the gradient leads to different learning behaviors. Therefore, it is possible to stably learn about any moment using the old GAN.

(Secondary theorem 2)

(Secondary Theorem 2) means that using a hypersphere is a reasonable choice to stably learn GAN.

In the above description, W of WGAN is'Wasserstein', which is used as a metric that compares the distance between a probability measure of an actual image and a probability measure of a generated image using a Westerstein distance.

In the present invention, a slightly larger range of metrics is defined to solve the problems of these technologies.

The metric used in the present invention is defined as the same as in Equation 9 described above as IPM (Integral Probability Metrics).

If f is a 1-Lipschitz function in Equation 9, the Wasserstein distance can be thought of as a type of IPM.

In the present invention, f is a distance function defined as in Equation (12). At this time, the distance function is the distance function between two points on the sphere.

This means that it is no longer necessary to satisfy the 1-Lipschitz condition, which means that there is no need to use a gradient penalty.

Equation 12 shows that in the previous WGAN-based techniques, when training a discriminator, the term C(x) of Equation 5 is added to limit capacity, whereas in the present invention, Equation As there is no additional term as in 6, there are fewer constraints on the discriminator network than the existing method, and accordingly, the performance of the same neural network is better.

The data processing method using the hostile generation network on the sphere through geometric moment matching according to the present invention will be described in detail as follows.

3 is a flow chart showing a data processing method using a hostile generation network on a sphere through geometric moment matching according to the present invention.

First, the generator receives a value from a random noise z to generate an image (fake data) similar to the real thing (S301).

Subsequently, the fake data generated by the generator is transmitted to the discriminator (S302).

Then, the discriminator receives real data and fake data, trains it, and maps it to an n-dimensional Euclidean feature space (S303).

Subsequently, the feature points of the fake sample and the real sample are respectively mapped back to the n-dimensional hypersphere by geometric transformation (S304).

Then, using the mapped points, the spherical GAN calculates the geometric moment centered on the north pole of the hypersphere (S305).

Subsequently, the discriminator of the old GAN tries to maximize the moment difference in the probability measurement between the real and fake samples, and the generator attempts to interfere with the discriminator by minimizing the moment difference to train (S306).

The performance evaluation results of the data processing apparatus and method using the hostile generation network on the sphere through geometric moment matching according to the present invention described above are as follows.

4 is a graph showing evaluation results according to different dimensions and moment matching modes of a hypersphere using IS (Inception scores).

,

,

모멘트 매칭모드를 나타낸 것이고, 가로축은 초구(hypersphere)

의 차원을 나타낸 것으로,n = 16, 64, 256, 1024이다.Red, yellow and blue bars are respectively

,

,

It shows the moment matching mode, and the horizontal axis represents the hypersphere.

It shows the dimension of, n = 16, 64, 256, 1024.

5 is a gradient characteristic graph of Sphere GAN and WGAN-GP discriminator network.

Table 3 below shows the results of CIFAR-10's unsupervised image generation. The higher the IS (Inception Scores) and the lower the FID (Frechet Inception Distance), the better the results.

As shown in Table 3, which shows quantitative results in CIFAR-10, the old GAN-ResNet has the latest records, and it can be seen that there is a big difference between both IS and FID, and the old GAN-Conv has WGAN-GP and MMD. The results are much better than GAN.

Table 4 below shows the results of unsupervised image creation in STL-10.

In the STL-10 experiment, about half of the number of network parameters were used compared to the original network, and despite the small number of network parameters, the old GAN-ResNet shows SN-GAN and other IPM-based GANs, as shown in Table 4. It shows better performance.

Table 5 below shows the results of unsupervised image creation in LSUN bedroom.

In the LSUN bedroom experiment, IS is meaningless, so only FID is shown, showing that the older GAN-ResNet outperforms the most advanced GAN.

And Figure 6 is a graph comparing the average calculation time repeated 100 times for different GAN variants.

The yellow and red bars show the average calculation time when the update ratios of the generator and the discriminator are 1:1 and 1:5, respectively.

7A and 7B are qualitative results of the old GAN for the LSUN-bedroom data set and the qualitative results for the STL-10 data set.

As can be seen from the evaluation results, the network proposed in the present invention is a hostile generation network that is a part of the generation model, which is a sub-field of machine learning and computer vision, and solves the problems of the prior art through mathematical modeling to speed up training. And has extensibility.

Accordingly, it is possible to generate data suitable for the site through the technology proposed in the present invention in the industrial field, and by having a fast execution speed, it is excellently extended by a simple structure, especially when used for purposes other than image data such as 3D, audio processing, etc. Have a surname

A data processing apparatus and method using a hostile generation network on a sphere through geometric moment matching according to the present invention described above relates to a generic adversarial network that is one of a generation model that is a sub-field of machine learning and computer vision. The GAN discriminator, which distinguishes real data from fake data, is configured to map the final data to a sphere and the distance by mapping the final data to a sphere. It is to enable stable GAN learning by using the configuration that calculates and using a distance bound.

It will be understood that the present invention is implemented in a modified form without departing from the essential characteristics of the present invention as described above.

Therefore, the specified embodiments are to be considered in terms of explanation rather than limitation, and the scope of the present invention is shown in the claims rather than the foregoing description, and all differences within the equivalent range are included in the present invention. Should be interpreted.

100. Generator
200. Discriminator
300. Geometric moment matching unit

Claims (15)

A generator that receives a value from random noise z to generate fake data and delivers the generated fake data to a discriminator;
A discriminator that receives and trains real data (x) and fake data;
The final data is received from the discriminator and mapped to the n-dimensional Euclidean feature space, respectively, and the feature points of the fake data and real data are re-mapped to n-dimensional hyperspheres by geometric transformation, and the mapped points are used. Includes a geometric moment matching unit for calculating the geometric moment centered on the north pole of the hypersphere (hypersphere) with a spherical GAN;
The discriminator attempts to maximize the moment difference in probability measurement between real and fake data, and the generator attempts to interfere with the discriminator by minimizing the moment difference to train the hostile generation network on the sphere through geometric moment matching. Data processing device used. The method of claim 1, wherein the spherical GAN is characterized in that it is possible to predict the behavior of a trained network by minimizing multi-order moments on the assumption that the feature space of the discriminant network is a sphere, and newly defining metrics between mathematically defined measures. A data processing device using a hostile generation network on a sphere through geometric moment matching. According to claim 1, The geometric moment matching unit,
The first moment in the one-dimensional feature space

Is defined as,
Here, G and D represent generators and discriminators, respectively, and P and N represent actual data and potential code distributions, respectively.
The discriminator (D) maps data (x) to real (R),

Is defined as,
Here, D must satisfy the 1-Lipschitz condition D ∈ Lip1, and X ⊂ Rn is based on n-dimensional Euclidean image space. Data processing apparatus using a hostile generation network on a sphere through geometric moment matching, characterized in that to match the moment. The output of the discriminator according to claim 3,

Is defined as,
Where x is the actual image data, z is a random data processing device using a hostile generation network on a sphere through geometrical moment matching characterized in that the noise. The objective function of claim 4, wherein the objective function of the sphere GAN is:

Is defined as,
Function if r = 1, ..., R

Indicates the measurement of the r-th moment distance between each sample and the north pole of the hypersphere N, and the subscript s is

end

Data processing apparatus using a hostile generation network on a sphere through geometric moment matching, characterized in that it is defined on the image. The method according to claim 5, wherein the spherical GAN does not require additional constraints to place the discriminator in the desired function space,
Using a geometric transformation, the spherical GAN ensures that the distance function is in the desired function space,
The new objective function of the discriminator

Data processing apparatus using a hostile generation network on a sphere through geometric moment matching, characterized in that defined as. 7. The sphere of claim 6, wherein the spherical GAN is a hypersphere.

Matching multiple moments through the feature space defined in
The old GAN uses a hypersphere instead of an arbitrary Lehmann manifold M,
Distance function of hypersphere

To form a bound,
The gradient norm works as a distance function,
A data processing apparatus using a hostile generation network on a sphere through geometric moment matching, characterized in that it defines a GAN object through a Riemannian structure of a hypersphere. 7. The method of claim 6, wherein the spherical GAN is a Euclidean space

The hypersphere

Use the geometric transformation function to convert to,
The conversion function

in

A data processing device that uses a hostile generation network on a sphere through geometric moment matching, which is designed by diffeomorphism to reach and is capable of differentiating and preserving dimensions at all points in the feature space. The method of claim 8, using a stereographic projection (stereographic projection) as a geometric transformation function,
The inverse function of stereographic projection is the Euclidean space

The hypersphere

Is diffeomorphism,

If the coordinate system of is p = (p1, ..., pn), and the north pole of the hypersphere is N = (0, ..., 1),
Inverse function of stereographic projection

silver,

Data processing apparatus using a hostile generation network on a sphere through geometric moment matching, characterized in that defined by. 10. The method of claim 9, wherein the two points through the inverse function of the stereographic projection (stereographic projection)

After projecting, measuring the distance between two points in terms of the hypersphere metric,

Is defined as,
here,

The

Is the distance function defined in Geometrically

Is a data processing device using a hostile generation network on a sphere through geometric moment matching, characterized in that it is considered as a geodetic distance. 11. The method of claim 10, To minimize the metric IPM (Integral Probability Metrics) used in the old GAN,
Define the geometric center moment for the Riemannian manifold, M is a small, connected, geodetically complete Riemann manifold with Borel σ algebra, Σ,

Wow

Is a probability measure defined in the measurable space (M, Σ), and both probability measures

Wow

IPM, the distance measurement between,

Is defined as,
F is a class of actual value boundary measurement functions for M. A data processing device using a hostile generation network on a sphere through geometric moment matching. 12. The method of claim 11, when defining a geometric moment for M.
(M, Σ) on given point p ₀

The r th center moment of

Is defined as,
here,

And

ego,

Is a Riemannian distance function in M. A data processing apparatus using a hostile generation network on a sphere through geometric moment matching. The method of claim 12, wherein the spherical GAN

Wow

If you define a new IPM between,
IPM based on moment difference,

Is defined as,
here,

Is a class of bounded distance functions from another point at a given point p _{0. A} data processing device using a hostile generation network on a sphere through geometric moment matching. 14. The method of claim 13, wherein the functional space of the IPM

Is a limited set of distance functions on the M phase centered on, and the spherical GAN parameterizes the distance function,

ego,
Where {xi} is a set of images,
If you parameterize the discriminator,

ego,
here,

Data processing apparatus using a hostile generation network on a sphere through geometric moment matching, characterized in that. Assuming that the feature space of the discriminant network is a sphere, using a spherical GAN that minimizes multi-order moments on top of it and newly defines metrics between mathematically defined measures to predict the behavior of the trained network.
Generating a fake data similar to the real by taking a value from the random noise z in the generator;
Passing the fake data generated by the generator to the discriminator;
The discriminator receives and trains real data and fake data and maps it to an n-dimensional Euclidean feature space;
Mapping the feature points of the fake data and the real data, respectively, to n-dimensional hyperspheres by geometric transformation;
Using the mapped points, the spherical GAN calculates the geometric moment centered on the north pole of the hypersphere;
The discriminator of the spherical GAN attempts to maximize the moment difference in the probability measurement between the real and fake samples, and the generator attempts to interfere with the discriminator by minimizing the moment difference to train the discriminator through geometric moment matching. Data processing method using a hostile generation network on a sphere.

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